Triplet with aspheric surfaces

ABSTRACT

A three element lens comprising two outer positive meniscuses and a central negative meniscus with all three elements concave to the aperture stop between the negative meniscus and a positive element.

This invention relates to lenses and more particularly relates to a three-element lens form.

LENSES HAVE TRADITIONALLY BEEN MADE OF GLASS WHICH REQUIRES GRINDING AND POLISHING OF THE SURFACES. In order to reduce the manufacturing costs of such lenses, designers have chosen lens forms which have a large ratio of surface radius to diameter to permit the grinding of an increased number of lenses at once.

The use of aspheric lens surfaces permits the optical designer greater latitude in designing a lens to given specifications. However, except for special purpose lenses the cost of producing aspherical surfaces on glass is prohibitive. When lens elements are of molded plastic, aspheric surfaces may be advantageously utilized with little if any increase in per unit cost.

Where wide field angle and fast relative aperture of the lens is not critical a three-element lens form known as the Cooke or Taylor triplet is most often utilized by designers. This triplet comprises a bi-convex element, and a bi-concave element followed by a third bi-convex element. This lens form provides many degrees of aberration correction for the designer. In this triplet form of lens the negative element generally has weak curvature to minimize manufacturing cost, and the limiting aberration in this form of lens for design purposes has been astigmatism.

The use of aspheric surfaces, which is generally permitted only in molded plastic lenses, has generally led to modifications of the Cooke or Taylor triplet by making aspheric one or more surfaces thereon as exemplified in U.S. Pat. Nos. 3,784,287, 3,912,379 and 3,944,337. The provision of aspheric surfaces as shown in these patents permits wider relative apertures, but the field angle is still quite limited without introduction of zonal astigmatism.

The present invention provides a new three-element lens of increased field angle with respect to the Cooke triplet, and permits large relative apertures and may include one or more aspheric surfaces.

Briefly stated, a lens embodying the invention comprises a first positive meniscus, a second negative meniscus followed by an aperture and then a third positive meniscus, or vice versa. All elements are concave toward the aperture. The lens may be utilized as described or inverted. Any or all of the surfaces can be made aspheric for increased aperture.

It is an object of this invention to provide a new and improved three-element lens having increased field angle.

Another object of this invention is to provide a new three-element lens using only meniscus elements.

A further object of this invention is to provide a three-element lens which is well corrected for astigmatism, and permits wide relative aperture with increased field angle.

The features of the invention which are believed to be novel are particularly pointed out and distinctly claimed in the concluding portion of this specification. The invention, however, both as to its organization and operation together with further objects and advantages thereof may best be appreciated by reference to the following detailed description taken in conjunction with the drawings, wherein:

FIG. 1 is a schematic side elevation of a first lens embodying the invention;

FIG. 2 is a schematic side elevation of another lens which in form is inverse to that of FIG. 1.

FIG. 3 is a diagram of the shape of surfaces which may be presented for lenses embodying the invention.

FIG. 4 is a schematic side elevation of a lens embodying the invention with at least one aspheric surface; and

FIG. 5 is a schematic side elevation of a lens which is the inverse of the lens of FIG. 4.

FIG. 6 is a schematic side elevation of another lens embodying the invention.

As shown in FIG. 1 a lens embodying the invention consists of three elements L1, L2, and L3 with an aperture stop A between the facing concave surface which may or may not be adjustably defined by an iris I.

The elements L1 - L3 have surfaces S1 - S6 defined on radii R1, R2; R3, R4; and R5, R6; respectively.

In the various figures, the lenses are shown with the light originating from the left.

The surfaces of all lenses will hereinafter be defined in terms of curvature C, where

    C = EFL/R

and EFL is the focal length of the overall lens, and R is the radius, or base radius at the optical axis if the surface is aspheric.

Two lenses of the form shown in FIG. 1 are defined by prescription in Tables I and II following. In the tables the equivalent focal length (EFL) of each element L1, L2 and L3 is given by F₁, F₂, and F₃, and EFL is given by F_(o).

In the following tables the index of refraction of the elements is given by N_(d) and the Abbe number by V_(d). The back focal length of the lens is indicated by BFL.

A lens as shown in FIG. 1 scaled to an EFL F_(o) = 23.4 for a semi-field angle of 23°, and a maximum relative aperture of f/8.0 is described substantially as follows in Table I.

                  TABLE I                                                          ______________________________________                                              Surface     Axial Distance                                                Lens Radius (mm) Between Surfaces (mm)                                                                          N.sub.D                                                                              V.sub.D                                 ______________________________________                                              R1 5.426                                                                  L1               1.800           1.490 57.0                                         R2 11.588                                                                                  0.250                                                              R3 4.629                                                                  L2               1.373           1.589 30.7                                         R4 2.663                                                                                   4.422                                                              R5 -6.971                                                                 L3               1.854           1.490 57.0                                         R6 -4.197                                                                 BFL 18.6                                                                       F.sub.1   = 18.960 mm     Cl = 4.31                                            F.sub.2   = -14.349 mm    C2 = 2.02                                            F.sub.3   = 17.605 mm     C3 = 5.06                                            F.sub.1 /F.sub.o                                                                         = .810          C4 = 8.79                                            F.sub.2 /F.sub.o                                                                         = -.613         C5 = -3.56                                           F.sub.3 /F.sub.o                                                                         = .752          C6 = -5.58                                           ______________________________________                                    

A lens as shown in FIG. 1 scaled to an EFL F_(o) = 25.5mm for a semi-field angle of 22°, and a maximum relative aperture of f/8.0 is described substantially as follows in Table II.

                  TABLE II                                                         ______________________________________                                              Surface     Axial Distance                                                Lens Radius (mm) Between Surfaces (mm)                                                                          N.sub.D                                                                              V.sub.D                                 ______________________________________                                              R1 5.665                                                                  L1               2.092           1.490 57.0                                         R2 11.576                                                                                  0.143                                                              R3 4.711                                                                  L2               1.524           1.589 30.7                                         R4 2.701                                                                                   4.384                                                              R5 -7.567                                                                 L3               2.155           14.90 57.0                                         R6 -4.371                                                                 BFL 18.3                                                                       F.sub.1   =  20.24 mm     Cl = 4.15                                            F.sub.2   = -14.92 "      C2 = 2.03                                            F.sub.3   = 17.23 "       C3 = 4.99                                            F.sub.1 /F.sub.0                                                                         = .861          C4 = 8.71                                            F.sub.2 /F.sub.0                                                                         = -.634         C5 = -3.11                                           F.sub.3 /F.sub.0                                                                         = .733          C6 = -5.38                                           ______________________________________                                    

FIG. 2 represents a lens which is of a form inverse to that of FIG. 1. For simplicity of disclosure and consistency, the lenses hereinafter inverse to that of FIG. 1 described are labeled with reference characters commencing L1, R1, S1, from the right, with the positive radii being considered as struck on a point to the left.

A lens as shown in FIG. 2 scaled to an EFL F_(o) = 23.0mm for a semi-field angle of 22°, and a maximum relative aperture of f/8.0 is described substantially as follows in Table III.

                  TABLE III                                                        ______________________________________                                              Surface     Axial Distance                                                Lens Radius(mm)  Between Surfaces(mm)                                                                           N.sub.D                                                                              V.sub.D                                 ______________________________________                                              R1 5.393                                                                  L1               1.899           1.490 57.0                                         R2 12.852                                                                                  0.124                                                              R3 3.929                                                                  L2               1.377           1.589 30.7                                         R4 2.549                                                                                   5.032                                                              R5 -5.502                                                                 L3               1.869           1.490 57.0                                         R6 4.261                                                                  BFL 18.3                                                                       F.sub.1   = 17.46 mm      Cl = 4.26                                            F.sub.2   = -19.523 "     C2 = 1.79                                            F.sub.3   = 25.72 "       C3 = 5.85                                            F.sub.1 /F.sub.0                                                                         = .76           C4 = 9.02                                            F.sub.2 /F.sub.0                                                                         = -.85          C5 = -4.18                                           F.sub.3 /F.sub.0                                                                         = 1.12          C6 = -5.40                                           ______________________________________                                    

The lens designs shown in FIGS. 1 and 2 may have one or more surfaces made aspheric to provide a greater relative aperture. When aspheric, the lens surface in diametrical half section is defined by

    X -1/2 C(K+1)X.sup.2 -1/2 CY.sup.2 + G.sup.C.spsp.3 .sup./2 Y.sup.4 = 0

where

X is the abscissa along the optical axis

Y is the ordinate

C is the curvature at the optical axis and equals F_(o) /R.

r is the radius at the optical axis

K is a conic constant

G is a higher order constant and equal to zero if the surface is a conic section of rotation.

This above equation defines a conic section of rotation made by rotation of a section of a cone taken transverse to the axis of the cone. Otherwise stated, the quantity X is the sag of the surface from a reference plane at an ordinate or semi-aperture distance Y from the optical axis. The equation may include other higher order terms (HY⁶ , KY⁸) if desired.

FIG. 3 exemplifies surface curvatures that may be generated for different values of G.

Various values of K will produce surface sections as follows:

    ______________________________________                                         K      = 0          Spherical                                                  K      = -1         Parabolic                                                  K      = 0 to -1    Ellipse where smaller axis                                                     is vertical                                                K      = positive   Ellipse when smaller axis                                                      is horizontal                                              K      = >-1        Hyperbola                                                  ______________________________________                                    

A three-element photographic lens of the type described having one or more aspheric surfaces is shown in FIG. 4 comprising elements L1, L2, and L3, having surfaces S1 - S6, defined on radii R1 - R6, at least at the optical axis, Tables IV - VI define such lenses.

A lens as shown in FIG. 4 scaled to an EFL F_(o) = 23.0mm for a semi-field angle of 30°, and a maximum relative aperture of f/4.0 is described substantially as follows in Table IV.

                  TABLE IV                                                         ______________________________________                                              Surface     Axial Distance                                                Lens Radius (mm) Between Surfaces (mm)                                                                          N.sub.D                                                                              V.sub.D                                 ______________________________________                                              R1 5.355                                                                  L1               3.610           1.490 57.1                                         R2 16.291                                                                                  0.120                                                              R3 4.568                                                                  L2               0.726           1.589 30.8                                         R4 2.401                                                                                   5.412                                                              R5 -9.289                                                                 L3               1.160           1.490 57.1                                         R6 -4.342                                                                 BFL 17.0                                                                       Aspheric Surfaces                                                                               K           G                                                 ______________________________________                                         S1               -0.4175      0.04557                                          S3                0.2313     -0.01841                                          S4               -0.1513     -0.01787                                          F.sub.1   = 14.65mm       Cl = 4.295                                           F.sub.2   = -9.775 "      C2 = 1.412                                           F.sub.3   = 15.41 "       C3 = 5.035                                           F.sub.1 /F.sub.0                                                                         = .637          C4 = 9.579                                           F.sub.2 /F.sub.0                                                                         = -.425         C5 = -2.476                                          F.sub.3 /F.sub.0                                                                         = .67           C6 = -5.297                                          ______________________________________                                    

A lens as shown in FIG. 4 scaled to an EFL F_(o) = 100mm for a semi-field angle of 22°, and a maximum relative aperture of f/4.0 is described substantially as follows in Table V.

                  TABLE V                                                          ______________________________________                                              Surface     Axial Distance                                                Lens Radius (mm) Between Surfaces (mm)                                                                          N.sub.D                                                                              V.sub.D                                 ______________________________________                                              R1 23.809                                                                 L1               15.667          1.490 57.1                                         R2 84.818                                                                                  .521                                                               R3 20.568                                                                 L2               3.151           1.589 30.8                                         R4 10.663                                                                                  23.375                                                             R5 -38.565                                                                L3               5.034           1.490 57.1                                         R6 -18.741                                                                BFL 73.8                                                                       Apheric Surfaces K           G                                                 ______________________________________                                         S1               -0.4227      0.0361                                           S3                0.1626     -0.00688                                          S4               -0.1586     -0.0152                                           F.sub.1   = 62.14 mm      Cl = 4.200                                           F.sub.2   = -42.56 "      C2 = 1.179                                           F.sub.3   = 68.53 "       C3 = 4.862                                           F.sub.1 /F.sub.0                                                                         = .6214         C4 = 9.378                                           F.sub.2 /F.sub.0                                                                         = -4.256        C5 = -2.593                                          F.sub.3 /F.sub.0                                                                         = .6853         C6 = -5.336                                          ______________________________________                                    

A lens as shown in FIG. 4 scaled to an EFL F_(o) = 50.1mm for a semi-field angle of 20°, and a maximum relative aperture of f/3.5 is described substantially as follows in Table VI.

                  TABLE VI                                                         ______________________________________                                              Surface     Axial Distance                                                Lens Radius (mm) Between Surfaces (mm)                                                                          N.sub.D                                                                              V.sub.D                                 ______________________________________                                              R1 10.338                                                                 L1               5.042           1.490 57.9                                         R2 39.274                                                                                  0.250                                                              R3 10.048                                                                 L2               1.500           1.590 30.7                                         R4  5.640                                                                                  15.465                                                             R5 -20.773                                                                L3               2.673           1.490 57.9                                         R6 -11.551                                                                BFL 32.43mm                                                                    Aspheric Surfaces                                                                               K           G                                                 ______________________________________                                         S1               -0.621      0                                                 S4               -0.322      0                                                 F.sub.1   = 26.99mm       C1 = 4.84                                            F.sub.2   = -24.94mm      C2 = 1.27                                            F.sub.3   = 48.37mm       C3 = 4.98                                            F.sub.1 /F.sub.0                                                                         = .539          C4 = 8.88                                            F.sub.2 /F.sub.0                                                                         = -.498         C5 = -2.41                                           F.sub.3 /F.sub.0                                                                         = .966          C6 = -4.33                                           ______________________________________                                    

A lens as shown in FIG. 4 scaled to an EFL F_(o) = 50mm for a semi-field angle of 20°, and a maximum relative aperture of f/3.5 is described substantially as follows in Table VII.

                  TABLE VII                                                        ______________________________________                                              Surface     Axial Distance                                                Lens Radius (mm) Between Surfaces (mm)                                                                          N.sub.D                                                                              V.sub.D                                 ______________________________________                                              R1 10.910                                                                 L1               5.462           1.490 57.9                                         R2 39.480                                                                                  .250                                                               R3  9.995                                                                 L2               1.50            1.590 30.7                                         R4  5.648                                                                                  15.501                                                             R5 -23.139                                                                L3               2.391           1.490 57.9                                         R6 -11.564                                                                BFL 34.0                                                                       Apheric Surfaces K           G                                                 ______________________________________                                         S1               -0.6350     0                                                 S4               -0.3220     0                                                 F.sub.1   = 28.95         C1 = 4.58                                            F.sub.2   = -29.90        C2 = 1.27                                            F.sub.3   = 44.18         C3 = 5.00                                            F.sub.1 /F.sub.0                                                                         = .579          C4 = 8.85                                            F.sub.2 /F.sub.0                                                                         = -.598         C5 = 2.16                                            F.sub.3 /F.sub.0                                                                         = .884          C6 = 4.32                                            ______________________________________                                    

The lens may be inverted from the form of FIG. 4 to the form of FIG. 5. Examples of such lenses are set forth in Tables VIII - XI.

In the lenses of Tables VII - X the first element L1 is to the right and positive radii are struck from the left.

A lens as shown in FIG. 5 scaled to an EFL F_(o) = 23.0mm for a semi-field angle of 22°, and a maximum relative aperture of f/8.0 is described substantially as follows in Table VIII.

                  TABLE VIII                                                       ______________________________________                                              Surface     Axial Distance                                                Lens Radius (mm) Between Surfaces(mm)                                                                           N.sub.D                                                                              V.sub.D                                 ______________________________________                                              R1 4.159                                                                  L1               2.809           1.490 47.0                                         R2 12.374                                                                                   .124                                                              R3 4.747                                                                  L2                .749           1.589 30.7                                         R4 2.435                                                                                   5.425                                                              R5 -5.834                                                                 L3               1.188           1.490 57.0                                         R6 -3.991                                                                 BFL 18.3                                                                       Aspheric Surfaces                                                                               K           G                                                 ______________________________________                                         S1               -0.2392     0                                                 F.sub.1   = 11.45 mm      C1 = 5.53                                            F.sub.2   = -9.63 "       C2 = 1.86                                            F.sub.3   = 21.22 "       C3 = 4.85                                            F.sub.1 /F.sub.0                                                                         = .50           C4 = 9.45                                            F.sub.2 /F.sub.0                                                                         = -.42          C5 = -3.94                                           F.sub.3 /F.sub.0                                                                         = .922          C6 = -5.76                                           ______________________________________                                    

A lens as shown in FIG. 5 scaled to an EFL F_(o) = 20.0mm for a semi-field angle of 20° and a maximum relative aperture of f/3.7 is described substantially as follows in Table IX.

                  TABLE IX                                                         ______________________________________                                              Surface     Axial Distance                                                Lens Radius (mm) Between Surfaces (mm)                                                                          N.sub.D                                                                              V.sub.D                                 ______________________________________                                              R1 3.509                                                                  L1               2.400           1.490 57.9                                         R2 24.623                                                                                  0                                                                  R3 3.976                                                                  L2                .916           1.588 30.6                                         R4 2.201                                                                                   8.393                                                              R5 -7.292                                                                 L3                .851           1.490 57.9                                         R6 -5.243                                                                 BFL 16.4                                                                       Aspheric Surfaces                                                                               K           G                                                 ______________________________________                                         S1               -.8897      0                                                 S4               -.4404      0                                                 F.sub.1   = 8.03mm        C1 = 5.70                                            F.sub.2   = -8.73         C2 =  .812                                           F.sub.3   = 33.42         C3 = 5.03                                            F.sub.1 /F.sub.0                                                                         = .40           C4 = 9.07                                            F.sub.2 /F.sub.0                                                                         =0 -.44         C5 = -2.74                                           F.sub.3 /F.sub.0                                                                         = 1.67          C6 = -3.81                                           ______________________________________                                    

A lens as shown in FIG. 5 scaled to an EFL F_(o) = 20.0mm for a semi-field angle of 20°, and a maximum relative aperture of f/3.7 is described substantially as follows in Table X.

                  TABLE X                                                          ______________________________________                                              Surface     Axial Distance                                                Lens Radius (mm) Between Surfaces (mm)                                                                          N.sub.D                                                                              V.sub.D                                 ______________________________________                                              R1 3.794                                                                  L1               1.106           1.613 58.6                                         R2 20.140                                                                                  0                                                                  R3 4.432                                                                  L2               .196            1.648 33.9                                         R4 2.407                                                                                   3.260                                                              R5 -6.312                                                                 L3               .851            1.613 58.6                                         R6 -5.29                                                                  BFL 19.0                                                                       Aspheric Surfaces                                                                               K           G                                                 ______________________________________                                         S1                 .7515     0                                                 S4                -.5595     0                                                 S6               -1.5242     0                                                 F.sub.1   = 7.435         C1 = 5.27                                            F.sub.2   = -8.451        C2 = 3.17                                            F.sub.3   = 40.50         C3 = 4.51                                            F.sub.1 /F.sub.0                                                                         = .371          C4 = 8.31                                            F.sub.2 /F.sub.0                                                                         = -.423         C5 = -3.17                                           F.sub.3 /F.sub.0                                                                         = 2.025         C6 = -3.78                                           ______________________________________                                    

A lens as shown in FIG. 5 scaled to an EFL F_(o) = 20.0mm for a semi-field angle of 20°, and a maximum relative aperture of f/3.7 is described substantially as follows in Table XI.

                  TABLE XI                                                         ______________________________________                                              Surface     Axial Distance                                                Lens Radius (mm) Between Surfaces (mm)                                                                          N.sub.D                                                                              V.sub.D                                 ______________________________________                                              R1 3.326                                                                  L1               2.400           1.490 57.9                                         R2 25.211                                                                                  0                                                                  R3 3.314                                                                  L2                .196           1.588 30.6                                         R4 1.905                                                                                   8.752                                                              R5 -6.793                                                                 L3                .851           1.490 57.9                                         R6 -5.160                                                                 BFL 17.2                                                                       Aspheric Surfaces                                                                               K           G                                                 ______________________________________                                         S1               1.0895      0                                                 S3               -.2499      0                                                 S4               -.5736      0                                                 F.sub.1   = 7.53mm        C1 = 6.03                                            F.sub.2   = -8.02"        C2 = .793                                            F.sub.3   = 37.32 "       C3 = 6.04                                            F.sub.1 /F.sub.0                                                                         = .377          C4 = 10.50                                           F.sub.2 /F.sub.0                                                                         = -.401         C5 = -2.94                                           F.sub.3 /F.sub.0                                                                         = 1.87          C6 = -3.88                                           ______________________________________                                    

A lens in accordance with the invention may be used in either the form shown in FIGS. 1 and 4, or in the inverted form of FIGS. 2 and 5, for either taking or projection.

Surfaces S4, S5 and S8 are aspheric. The aperture stop defining member A is disposed between elements L2 and L3, as previously disclosed. This lens, with the addition of L4 may be designed with a relative aperture of f/2.8. The third L3 element adds more negative power to the lens and gives a better tool for color correction.

From the foregoing examples it may be seen that the value of the ratio of the Abbe values of the positive lens to that of the negative lens is always greater than 1.8 or

    (V.sub.= /V.sub.-) > 1.8

this permits the lens to be achromatized. Any of the surfaces can be made aspheric for increased relative aperture. The lens is basically well corrected for astigmatism, the one limiting aberration of the Cooke triplet.

The distance D4 between the facing concave surfaces of elements L2 and L3 is

    0.10F.sub.o ≦ D.sub.4 ≦ 0.50F.sub.o

where F_(o) is the EFL of the overall lens.

Additionally, the distance D₂ between elements L1 and L2 in the range is

    0 ≦ D.sub.2 ≦ 0.2F.sub.o

The EFL's of the elements bear the following relation:

    0.35F.sub.o ≦ F.sub.1 ≦ 1.0F.sub.o

    0.35F.sub.o ≦ |F.sub.2 | ≦  1.0F.sub.o

    0.50 ≦ F.sub.3 ≦ 2.0F.sub.o

    F.sub.o > F.sub.1

    f.sub.o > |F.sub.2 |

the curvatures of the lens surfaces are:

    C1 ≧ 4.0

    c1 ≧ c2 ≧ 0.7

    c4 > c3 ≧ 4.5

    c3 < c4 ≧ 8.0

    |c5| ≧ 2.0

    |c6| ≧ 3.5

the elements having aspheric surfaces are preferably molded of a suitable plastic such as polymethyl methacrylate, polycyclohexyl methacrylate, polystyrene or acrylonitrile. The elements not having aspheric surfaces may be glass or plastic.

As will be seen from the examples set forth, one or more of any and all of the lenses may be made aspheric. In all cases a semi-field angle of at least 20° is achieved.

It may thus be seen that the objects of the invention set forth as well as those made apparent from the foregoing description are efficiently attained. While preferred embodiments of the invention have been set forth for purposes of disclosure, modification to the disclosed embodiments of the invention as well as other embodiments thereof may occur to those skilled in the art. Accordingly, the appended claims are intended to cover all embodiments of the invention and modifications to the disclosed embodiments which do not depart from the spirit and scope of the invention. 

What is claimed is:
 1. A lens consisting of first, second and third elements, said first and third elements being meniscuses of positive power with facing concave surfaces, said second element being a meniscus of negative power between said first and third elements, an aperture defining means between the concave surface of said second element and the concave surface of one of said other elements, the elements commencing with the positive element removed from the aperture defining means have equivalent focal lengths F1, F2 and F3, and:

    F.sub.o > F.sub.1

    f.sub.o > |F.sub.2 |

    0.5f.sub.o ≦ F.sub.3 ≦ 2.1F.sub.o

where F_(o) is the equivalent focal length of the overall lens.
 2. The lens of claim 1 having surface curvatures C1-C6 successively from the element separated from the aperture by the negative element where C = F/R, F is the equivalent focal length of the lens, R is the surface radius of the element at the optical axis, and

    7.0 > C1 > 4.0

    11.0 < c4 > 8.0


3. the lens of claim 2 where

    7.0 > C3 > 4.5

    4.5 > c5 > 2.0

    6.0 > c6 > 3.5

    c6 > |c5|


4. the lens of claim 1 where the Abbe number of the positive elements is at least 1.8 times the Abbe number of the negative element.
 5. The lens of claim 1 wherein the distance D₂ between the convex side of the negative element and the adjacent positive element is:

    0 ≦ D.sub.2 < 0.02F.sub.o

where F_(o) is the equivalent focal length of the lens.
 6. The lens of claim 1 wherein the distance D₄ on the optical axis between the facing concave surfaces on either side of the means defining the aperture is:

    0.1F.sub.o < D.sub.4 < 0.5F.sub.o .


7. The lens of claim 1 having surface curvatures C1-C6 successively from the element separated from the aperture by the negative element, where C = F/R, F is the focal length of the lens, R is the surface radius of the element at the optical axis, and

    7.0 > C1 > 4

    3.2 > c2 > 0.7

    7.0 > c3 > 4.5

    11.0 > c4 > 8.0

    4.5 > c5 > 2.0

    6.0 > c6 > 3.5.


8. the lens of claim 1 defined substantially as follows:

    ______________________________________                                                          Axial                                                         Lens Surface     Between Surfaces/EFL                                                                           N.sub.d                                                                              V.sub.d                                 ______________________________________                                              C1 4.31                                                                   L1               .077            1.490 57.0                                         C2 2.02                                                                                    .011                                                               C3 5.06                                                                   L2               .059            1.589 30.7                                         C4 8.79                                                                                    0.189                                                              C5 -3.56                                                                  L3               .080            1.490 57.0                                         C6 -5.58                                                                  ______________________________________                                    

where EFL is the equivalent focal length of the lens; L1-L3 are successive elements with L1 furtherest removed from the aperture, C1-C6 are successive surface curvatures of element L1-L3 where the curvature is the EFL of the lens divided by radius of the surface at the optical axis; N_(d) is the index of refraction and V_(d) is the Abbe number of the elements.
 9. The lens of claim 1 defined substantially as follows:

    ______________________________________                                                          Axial                                                         Lens Surface     Between Surfaces/EFL                                                                           N.sub.d                                                                              V.sub.d                                 ______________________________________                                              Cl 4.15                                                                   L1               .082            1.490 57.0                                         C2 2.03                                                                                    .006                                                               C3 4.99                                                                   L2               .060            1.589 30.7                                         C4 8.71                                                                                    0.172                                                              C5 -3.11                                                                  L3               .085            14.90 57.0                                         C6 -5.38                                                                  ______________________________________                                    

where EFL is the equivalent focal length of the lens; L1-L3 are successive elements with L1 furtherest removed from the aperture, C1-C6 are successive surface curvatures of element L1-L3 where the curvature is the EFL of the lens divided by radius of the surface at the optical axis; N_(d) is the index of refraction and V_(d) is the Abbe number of the elements.
 10. The lens of claim 1 defined substantially as follows:

    ______________________________________                                                          Axial                                                         Lens Surface     Between Surfaces/EFL                                                                           N.sub.d                                                                              V.sub.d                                 ______________________________________                                              C1 4.26                                                                   L1               .083            1.490 57.0                                         C2 1.79                                                                                    .005                                                               C3 5.85                                                                   L2               .060            1.589 30.7                                         C4 9.02                                                                                    .219                                                               C5 -4.18                                                                  L3               .081            1.490 57.0                                         C6 -5.40                                                                  ______________________________________                                    

where EFL is the equivalent focal length of the lens; L1-L3 are successive elements with L1 furtherest removed from the aperture, C1-C6 are successive surface curvatures of element L1-L3 where the curvature is the EFL of the lens divided by radius of the surface at the optical axis; N_(d) is the index of refraction and V_(d) is the Abbe number of the elements.
 11. The lens of claim 1 wherein at least a surface of one element is made aspheric and defined by:

    X-1/2C(K+1)X.sup.2 -1/2CY.sup.2 +G.sup.C.spsp.3 /2 Y.sub.4 = 0

where X is the sag of the surface from a reference plane at a semi-aperture distance Y from the optical axis; C is the curvature of the lens at the optical axis and equal to the equivalent focal length of the lens divided by the radius of curvature at the optical axis; K is a conic constant; and G is a constant coefficient of higher order aspheric sag of the surface and said elements have successive surfaces S1-S6 commencing with the positive element removed from the aperture defining means.
 12. The lens of claim 11 wherein the convex surface of the element removed from the aperture defining means is aspheric.
 13. The lens of claim 12 where

    0 > K > -1.


14. The lens of claim 11 wherein both surfaces S3 and S4 of the negative element are aspheric.
 15. The lens of claim 11 defined substantially as follows:

    ______________________________________                                                          Axial                                                         Lens Surface     Between Surfaces/EFL                                                                           N.sub.d                                                                              V.sub.d                                 ______________________________________                                              C1 4.295                                                                  L1               .157            1.490 57.1                                         C2 1.412                                                                                   .011                                                               C3 5.035                                                                  L2               .031            1.589 30.8                                         C4 9.579                                                                                   .235                                                               C5 -2.476                                                                 L3               .050            1.490 57.1                                         C6 -5.297                                                                 Aspheric Surfaces                                                                             K            G                                                  ______________________________________                                         S1             -0.4175       0.04557                                           S3              0.2313      -0.01841                                           S4             -0.1513      -0.01787                                           ______________________________________                                    

where EFL is the equivalent focal length of the lens; L1-L3 are successive elements with L1 furtherest removed from the aperture, C1-C6 are successive surface curvatures of elements L1-L3 at the optical axis where the curvature is the EFL of the lens divided by radius of the surface at the optical axis; and N_(d) is the index of refraction and V_(d) is the Abbe number of the elements.
 16. The lens of claim 11 defined substantially as follows:

    ______________________________________                                                          Axial                                                         Lens Surface     Between Surfaces/EFL                                                                           N.sub.d                                                                              V.sub.d                                 ______________________________________                                              C1 4.200                                                                  L1               .157            1.490 57.1                                         C2 1.179                                                                                   .005                                                               C3 4.862                                                                  L2               .031            1.589 30.8                                         C4 9.378                                                                                   .234                                                               C5 -2.593                                                                 L3               .050            1.490 57.1                                         C6 -5.336                                                                 Aspheric Surfaces                                                                             K            G                                                  ______________________________________                                         S1             -0.4227       0.0361                                            S3              0.1626       -0.00688                                          S4             -0.1586      -0.0152                                            ______________________________________                                    

where EFL is the equivalent focal length of the lens; L1-L3 are successive elements with L1 furtherest removed from the aperture, C1-C6 are successive surface curvatures of elements L1-L3 at the optical axis where the curvature is the EFL of the lens divided by radius of the surface at the optical axis; and N_(d) is the index of refraction and V_(d) is the Abbe number of the elements.
 17. The lens of claim 11 defined substantially as follows;

    ______________________________________                                                          Axial                                                         Lens Surface     Between Surfaces/EFL                                                                           N.sub.d                                                                              V.sub.d                                 ______________________________________                                              C1 4.84                                                                   L1               .101            1.490 57.9                                         C2 1.27                                                                                    .005                                                               C3 .498                                                                   L2               .030            1.590 30.7                                         C4 8.88                                                                                    .309                                                               C5 -2.41                                                                  L3               .053            1.490 57.9                                         C6 -4.33                                                                  Aspheric Surfaces                                                                             K            G                                                  ______________________________________                                         S1             -0.621       0                                                  S4             -0.322       0                                                  ______________________________________                                    

where EFL is the equivalent focal length of the lens; L1-L3 are successive elements with L1 furtherest removed from the aperture, C1-C6 are successive surface curvatures of elements L1-L3 at the optical axis where the curvature is the EFL of the lens divided by radius of the surface at the optical axis; and N_(d) is the index of refraction and V_(d) is the Abbe number of the elements.
 18. The lens of claim 11 defined substantially as follows:

    ______________________________________                                                          Axial                                                         Lens Surface     Between Surfaces/EFL                                                                           N.sub.d                                                                              V.sub.d                                 ______________________________________                                              C1 4.58                                                                   L1               .109            1.490 57.9                                         C2 1.27                                                                                    .005                                                               C3 5.00                                                                   L2               .030            1.590 30.7                                         C4 8.85                                                                                    .310                                                               C5 -2.16                                                                  L3               .048            1.490 57.9                                         C6 -4.32                                                                  Aspheric Surfaces                                                                             K            G                                                  ______________________________________                                         S1             -0.6350      0                                                  S4             -0.3220      0                                                  ______________________________________                                    

where EFL is the equivalent focal length of the lens; L1-L3 are successive elements with L1 furtherest removed from the aperture, C1-C6 are successive surface curvatures of elements L1-L3 at the optical axis where the curvature is the EFL of the lens divided by radius of the surface at the optical axis; and N_(d) is the index of refraction and V_(d) is the Abbe number of the elements.
 19. The lens of claim 11 defined substantially as follows:

    ______________________________________                                                          Axial                                                         Lens Surface     Between Surfaces/EFL                                                                           N.sub.d                                                                              V.sub.d                                 ______________________________________                                              C1          5.53                                                          L1               .122            1.490 47.0                                         C2 1.86                                                                                    .005                                                               C3 4.85                                                                   L2               .032            1.589 30.7                                         C4 9.45                                                                                    .236                                                               C5 -3.94                                                                  L3               .052            1.490 57.0                                         C6 -5.76                                                                  Aspheric Surfaces                                                                             K            G                                                  ______________________________________                                         S1             -0.2392      0                                                  ______________________________________                                    

where EFL is the equivalent focal length of the lens; L1-L3 are successive elements with L1 furtherest removed from the aperture, C1-C6 are successive surface curvatures of elements L1-L3 at the optical axis where the curvature is the EFL of the lens divided by radius of the surface at the optical axis; and N_(d) is the index of refraction and V_(d) is the Abbe number of the elements.
 20. The lens of claim 11 defined substantially as follows:

    ______________________________________                                                          Axial                                                         Lens Surface     Between Surfaces/EFL                                                                           N.sub.d                                                                              V.sub.d                                 ______________________________________                                              C1 5.70                                                                   L1               .120            1.490 57.9                                         C2  .812                                                                                   0                                                                  C3 5.03                                                                   L2               .010            1.588 30.6                                         C4 9.07                                                                                    .420                                                               C5 -2.74                                                                  L3               .043            1.490 57.9                                         C6 -3.81                                                                  Aspheric Surfaces                                                                             K            G                                                  ______________________________________                                         S1             -.8897       0                                                  S4             -.4404       0                                                  ______________________________________                                    

where EFL is the equivalent focal length of the lens; L1-L3 are successive elements with L1 furtherest removed from the aperture, C1-C6 are successive surface curvatures of elements L1-L3 at the optical axis where the curvature is the EFL of the lens divided by radius of the surface at the optical axis; and N_(d) is the index of refraction and V_(d) is the Abbe number of the elements.
 21. The lens of claim 11 defined substantially as follows:

    ______________________________________                                                          Axial                                                         Lens Surface     Between Surfaces/EFL                                                                           N.sub.d                                                                              V.sub.d                                 ______________________________________                                              C1 5.27                                                                   L1               .055            1.613 58.6                                         C2 3.17                                                                                    0                                                                  C3 4.51                                                                   L2               .010            1.648 33.9                                         C4 8.31                                                                                    .163                                                               C5 -3.17                                                                  L3               .043            1.613 58.6                                         C6 -3.78                                                                  Aspheric Surfaces                                                                             K            G                                                  ______________________________________                                         S1               .7515      0                                                  S4              -.5595      0                                                  S6             -1.5242      0                                                  ______________________________________                                    

where EFL is the equivalent focal length of the lens; L1-L3 are successive elements with L1 furtherest removed from the aperture, C1-C6 are successive surface curvatures of elements L1-L3 at the optical axis where the curvature is the EFL of the lens divided by radius of the surface at the optical axis; and N_(d) is the index of refraction and V_(d) is the Abbe number of the elements.
 22. The lens of claim 11 defined substantially as follows:

    ______________________________________                                                          Axial                                                         Lens Surface     Between Surfaces/EFL                                                                           N.sub.d                                                                              V.sub.d                                 ______________________________________                                              C1 6.03                                                                   L1               .120            1.490 57.9                                         C2  .793                                                                                   0                                                                  C3 6.04                                                                   L2               .010            1.588 30.6                                         C4 10.50                                                                                   .438                                                               C5 -2.94                                                                  L3               .043            1.490 57.9                                         C6 -3.88                                                                  Aspheric Surfaces                                                                             K            G                                                  ______________________________________                                         S1              1.0895      0                                                  S3             -.2499       0                                                  S4              .5736       0                                                  ______________________________________                                    

where EFL is the equivalent focal length of the lens; L1-L3 are successive elements with L1 furtherest removed from the aperture, C1-C6 are successive surface curvatures of elements L1-L3 at the optical axis where the curvature is the EFL of the lens divided by radius of the surface at the optical axis; and N_(d) is the index of refraction and V_(d) is the Abbe number of the elements. 